This paper investigates the uncertainty of machine tools and proposes an efficient interval uncertainty analysis framework for machine tools. This problem involves interval analysis and the calculation of machine tool response. The traditional analysis method has drawbacks, including low computational efficiency and the need to collect a large amount of sample information. In this paper, the intelligent optimization algorithm is used to analyze the interval of the machine tool, and the interval analysis results can be obtained by using less sample information, which improves the efficiency of the interval analysis. The dynamic evolution sequence (DES) is used to optimize the search sequence of the artificial bee colony (ABC) algorithm to improve the computational efficiency and accuracy of the optimization algorithm. To address the problem of the high computational cost of the finite element model, the Kriging surrogate model is used to replace complex finite element calculations. To achieve better calculation accuracy, this paper utilizes the DES to optimize the Kriging model, resulting in a significant improvement in the calculation accuracy of the improved Kriging model (DES-Kriging). Combining DES-ABC and DES-Kriging, this paper proposes a new interval uncertainty analysis framework and verifies the accuracy and efficiency of this interval analysis framework by numerical experiments.

To enhance the efficiency and accuracy of response analysis in practical multivariable complex engineering problems, we introduced a new interval analysis method—multi-body dynamic evolution sequence-assisted particle swarm optimization (DES-PSO) is introduced in this research. This method optimizes the heterogeneous comprehensive learning particle swarm optimization algorithm (HCLPSO) by incorporating a dynamic evolution sequence (DES), addressing the difficulty of HCLPSO in covering the search space, which makes this method suitable for solving multivariable interval analysis problems. The results of two numerical examples prove that both DES-PSO and HCLPSO can give the accurate upper and lower bounds of the response interval. Compared with HCLPSO, DES-PSO improves the computing speed by about 50%.